I just got round to having a look at John Cochrane's recent paper
on the neo-Fisherian hypothesis, that higher nominal interest rates raise
inflation. A main theme of this paper is
the issue of whether there is a theoretical basis for thinking that, even if this holds as a long-run equilibrium condition, the short
run impact is the reverse. It is
commonly believed that the initial response to a higher interest rate will be
lower inflation; Cochrane looks at whether we are right to think this.

The paper makes a good case that the basic New Keynesian
model does not in fact imply the conventional result. Cochrane also looks at several possible variations
but concludes that these do not providing a convincing case for an initial
deflation.

In my view, there is a very simple reason explanation of why
we might expect an initial deflation and it's to do with term debt. This is easy to see within Cochrane's model.

y

_{t}= E[y_{t+1}] { Î² ( 1 + i_{t}) / ( 1 + E[Ï€_{t+1}] ) }^{-Ïƒ}
1 + Ï€

_{t}= ( 1 + E[Ï€_{t+1}] )^{Î²}y_{t}^{Îº}
The third equation (the central bank reaction function) is
replaced with an interest rate peg.

Cochrane also considers the inclusion of a public sector
budget constraint:

B

_{t}= ( B_{t-1}- s_{t}p_{t}) ( 1 + i_{t })
where B
is the nominal stock of single period government debt by face value (which
we'll call bills), s is the real primary public sector surplus and p is the
price level. This accounting identity
can be extrapolated to show that the current real value of public debt is equal
to the discounted value of future primary surpluses. In turn, taking the historical level of
public debt together with expected future surpluses and real interest rates
gives us a current equilibrium price level, as follows:

p

_{t}= B_{t-1 }/ E[S_{t}]
where
E[S] is the expected present value of future surpluses.

Cochrane
uses this to distinguish between the multiple equilibria that are admitted by
the simple two equation model, but finds that this does not convincingly point
to an initial deflation.

From
looking at how SFC models work, the thing that I would do at this point is try
to incorporate some term debt. The
easiest way to do that here is to suppose that some part of the public debt
consists of an annuity which pays a fixed nominal amount. The public sector budget constraint (assuming
no new issue of annuities) is now:

B

_{t}= ( B_{t-1}+ a - s_{t}p_{t}) ( 1 + i_{t })
where a
is the nominal value of the annuity payment.
The equilibrium price level now becomes:

p

_{t}= ( B_{t-1 }+ A_{t }+ a ) / E[S_{t}]
where A is the nominal present value of the future annuity stream
based on expected future interest rates (and assuming here that this is valued
and discounted at the same rate as is paid on bills).

Examining this formula, we can see why a
rise in expected nominal interest rates might create an initial deflationary effect. Whilst the interest rate change has no impact
on the value of bills, it does effect the value of the annuity. A rise in expected nominal interest rates reduces the
value of the annuity and therefore reduces the equilibrium price level. If annuities make up a sufficient part of the
public debt, this results in an initial deflation.

The charts below show what this looks like in Cochrane's
model. I have used the same parameters and
the charts are the equivalent of Cochrane's Figure 1, but with 25% by value of
public debt assumed to be in the form of annuities.

The first chart shows the result of an expected increase in
the nominal rate. This chart is
essentially the same as Cochrane's Figure 1.
This is what we would expect, because if everything pans out in line
with expectations, there is no difference between bills and annuities.

The second chart shows the impact of an unexpected rate increase. This is very different. Not only do we get a much greater fall in real
output but we now also get a temporary fall in inflation. This is the result of the shock
revaluation of term debt.

Of course, this result should be of no surprise to anyone familiar with SFC modelling. These dynamics are typical of what happens in models which combine long run and short run debt and are relatively insensitive to assumptions about expectation formation or inter-temporal preference.

[Edited to conform a bit more closely to Cochrane.]

[Edited to conform a bit more closely to Cochrane.]

Is this the model that David Andolfatto thought was "very very interesting?" Did you email him your code?

ReplyDeleteO/T: Nick, I saw your comment on Nick Rowe's "framework" post. Do you also have a framework you work from? How would you describe it? Here's a criticism of Rowe's framework I read in another blog, and I'm curious what your opinion is:

"Nick Rowe jumps in with something that is also not a conceptual framework, but rather a vague model or a collection of priors. Among other things his framework for understanding macroeconomics -- where one of the big unsolved problems is what is a recession -- includes a specific definition and mechanism of a recession."

"If I said I was a doctor studying Alzheimer's and my conceptual framework included a tenet that Alzheimer's disease was defined by amyloid plaque build-up (rather than, say, the stereotypical symptom of memory loss) and lo and behold I put up some micrographs of amyloid plaque build-up in a neuron and said that caused Alzheimer's ... exactly what is my conceptual framework helping me understand?"

"A macroeconomic framework should not postulate what a recession is. You should use the framework to figure out what a recession is."

Hi Tom,

DeleteNo - David was interested in my take on the Diamond growth model, in my post from February. We've exchanged some brief emails, but he hasn't had a chance to look at it in any detail.

I think Nick Rowe's framework is fine for thinking about issues to do with the importance of monetary exchange. It would not be adequate for considering other issues. In my opinion, it's a mistake to limit yourself to one framework (and I'm not suggesting that Nick does so). You need to choose frameworks suitable to the task and ideally to look at things from multiple perspectives.

Thanks Nick. So I take it you use a variety of frameworks, perhaps including the one that Nick Rowe outlined?

DeleteYes, I'd have no problem using Nick's framework as one of a number of different approaches.

Delete